A111520 Sequence is {a(2,n)}, where a(m,n) is defined at sequence A111518.

1, 2, 0, -6, -5, 7, -43, -107, 410, -308, -5201, 22426, 1694, -462663, 2209642, 47303, -62434277, 381876639, -384111618, -11477555984, 100411394912, -284526009121, -2378813791310, 34944615773187, -187609218526529, -247374733853554, 14024268845995431

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Example

a(0,n): 1,0,-3,-4,7,...
a(1,n): 1,1,-2,-6,1,...
a(2,n): 1,2,0,-6,-5,...
a(3,n): 1,3,3,-3,-8,...
a(4,n): 1,4,7,4,-4,...
Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).

Maple

A111520T := proc(nmax) local a, m, n; a := array(0..nmax, 0..nmax) ; for m from 0 to nmax do a[m, 0] := 1 ; od ; for n from 1 to nmax do a[n, n] := a[0, n-1] ; for m from n+1 to nmax do a[m, n] := a[m-1, n]+a[m, n-1] ; od ; for m from n-1 to 0 by -1 do a[m, n] := a[m+1, n]-a[m+1, n-1] ; od ; od ; RETURN(a) ; end: nmax := 50 ; a := A111520T(nmax) ; r := 2 ; for n from 0 to nmax do printf("%d, ", a[r, n]) ; od; # R. J. Mathar, Sep 26 2006

Mathematica

nmax = 26;
a[_, 0] = 1;
a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1];
sol = Solve[Table[a[n + 1, n + 1] == a[0, n], {n, 0, nmax}], Table[a[0, n], {n, 1, nmax + 1}], Integers] // First;
Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];
Table[a[2, n], {n, 0, nmax}] (* Jean-François Alcover, Sep 21 2020 *)

Crossrefs

Cf. A111518, A111519, A111521, A111522, A111523.

Sequence in context: A211241 A140247 A271170 * A326040 A145419 A276763

Adjacent sequences: A111517 A111518 A111519 * A111521 A111522 A111523

Keyword

easy,sign

Author

Leroy Quet, Aug 05 2005

Extensions

More terms from R. J. Mathar, Sep 26 2006

Status

approved